Classical Communication using random unitary channels

We look at communication protocols where the parties involved face the restriction of a supers- election rule. We show how to circumvent superselection by doubling one party's state space and encoding information in the transformation that relates the rst state to the second. By requiring that all parties involved in the communication protocol agree on their assessment of the protocol's performance, we obtain closed-form expressions for the best encoding states and decoding measure- ments in the cases where the superselection rule is associated with a general nite group. We show that the optimal decoding measurements are joint measurements and the corresponding optimal states are entangled states.